Finite Group Databasebeta

← #27205539

Subgroups — #27205539

Order 13184.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268342C211yesmaximal, characteristic
2C4⋊Q8×D103C211yesmaximal, characteristic, complemented
3#20268152C214yesmaximal, complemented
4#20268141C211yesmaximal, characteristic, complemented
5#20268139C211yesmaximal, characteristic, complemented
6#20268138C211yesmaximal, characteristic, complemented
7#20267791C214yesmaximal, complemented
8C4×#13110088C211yesmaximal, characteristic, complemented
9#487×C103C211yesmaximal, characteristic, complemented
10C2×#13110106C2212yes—
11C2×Q8×D103—21no—
12C2×#13110088C2212yes—
13#15693021C2211yescharacteristic
14#15693020—21no—
15#15693020C2212yes—
16#15693019—21no—
17#15693018C2211yescharacteristic
18#15693010C2212yes—
19#15692996—21no—
20#15692996—21no—
21#15692983—21no—
22#15692983—21no—
23C4⋊C4×D103—21no—
24C4⋊C4×D103C2212yes—
25C42×D103C2211yescharacteristic
26#15692945C2214yes—
27#15692943C2214yes—
28#15692941C2214yes—
29#15692931C2212yes—
30C4×C103⋊C8C2211yescharacteristic
31C4⋊Q8×C103C2211yescharacteristic
32C4⋊Q8×C103C2211yescharacteristic
33#103×C103C2214yes—
34C4×C8×C103C2211yescharacteristic
35#13110106—28no—
36C2×Dic206—21no—
37C2×Dic206—22no—
38Q8×D103—44no—
39C2×D412—22no—
40C2×D412—21no—
41C2×D412—21no—
42C2×D412C2312yes—
43C2×C4×D103—22no—
44C2×C4×D103—22no—
45C2×C4×D103D411yescharacteristic
46C2×C4×D103D411yescharacteristic
47C2×C4×D103C2311yescharacteristic
48#13110088—24no—
49C2×C103⋊C8C2312yes—
50C4⋊Dic103—21no—
51C4⋊Dic103C2312yes—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54(C2×D103)⋊C4—22no—
55(C2×D103)⋊C4—22no—
56C4×Dic103D411yescharacteristic
57C4×Dic103D411yescharacteristic
58C4×Dic103C2311yescharacteristic
59C2×Q8×C103—21no—
60C2×Q8×C103C2312yes—
61C2×C8×C103C2312yes—
62C4⋊C4×C103—21no—
63C4⋊C4×C103—21no—
64C4⋊C4×C103—21no—
65C4⋊C4×C103C2312yes—
66C42×C103C2311yescharacteristic
67C22×D103—22no—
68C22×D103C2×D411yescharacteristic
69Q8×C103—24no—
70Q8×C103—42no—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2411yescharacteristic
76C2×Dic103—22no—
77C2×Dic103C2×D411yescharacteristic
78C2×Dic103C2×D411yescharacteristic
79C2×Dic103C2×D411yescharacteristic
80D412—24no—
81D412—44no—
82D412—42no—
83D412—42no—
84C4×D103—22no—
85C4×D103—22no—
86C4×D103—44no—
87C4×D103—44no—
88C4×D103#4114yes—
89Dic206—44no—
90Dic206—42no—
91C8×C103—22no—
92C103⋊C8—22no—
93C22×C103C22×D411yescharacteristic
94C2×D103—21no—
95C2×D103—21no—
96C2×D103—42no—
97C2×D103—42no—
98C2×D103—42no—
99C2×D103#12412yes—
100C4×C103—42no—
101C4×C103—42no—
102C4×C103AGL(1,ℤ/8)12yes—
103C4×C103#13712yes—
104C4×C103C2×#4112yes—
105Dic103—21no—
106Dic103—21no—
107Dic103—42no—
108Dic103#12412yes—
109C2×C103C2×#12411yescharacteristic
110C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C103C2×#13711yescharacteristic
112D103—22no—
113D103—82no—
114#3141—1031nomaximal, Sylow
115C103#314111yescharacteristic, complemented, Sylow
116#532—1031no—
117C2×C4⋊Q8—1031no—
118#489—1034no—
119#487—1031no—
120#487D10311yescharacteristic, complemented
121#486—1031no—
122#486—1031no—
123#417—1034no—
124C4×M16—1031no—
125C2×#41—1032no—
126C22×Q8—2061no—
127C2×M16—1032no—
128C4⋊Q8—1032no—
129C4⋊Q8—1031no—
130C4⋊Q8—2061no—
131C4⋊Q8—2061no—
132C4⋊Q8C2×D10311yescharacteristic
133C4⋊Q8C2×D10311yescharacteristic
134#127—1031no—
135#124—1032no—
136#121—2061no—
137#121—2061no—
138C4×D4—2061no—
139C4×D4—2061no—
140C2×C4⋊C4—1032no—
141C2×C4⋊C4—2061no—
142C2×C42—1031no—
143#103—1034no—
144#103C2×D10314yes—
145#102—1034no—
146#102—1034no—
147#97—1032no—
148C4×C8—1031no—
149C4×C8C2×D10311yescharacteristic
150#41—2068no—
151C2×Q8—21no—
152C2×Q8—4124no—
153C2×Q8—2062no—
154C2×Q8—2061no—
155C2×Q8C22×D10312yes—
156C2×D4—1032no—
157C2×D4—2062no—
158C2×D4—2061no—
159C2×D4—2061no—
160C22×C4—1031no—
161C22×C4—1031no—
162C22×C4—1031no—
163C22×C4—2062no—
164C22×C4—2062no—
165M16—2064no—
166C2×C8—1032no—
167C2×C8C22×D10312yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1032no—
172C4⋊C4—2062no—
173C4⋊C4—2062no—
174C4⋊C4—2061no—
175C4⋊C4C22×D10312yes—
176C22⋊C4—2062no—
177C22⋊C4—2062no—
178C42—1031no—
179C42—1031no—
180C42—1031no—
181C42C22×D10311yescharacteristic
182C23—1031no—
183C23—2062no—
184Q8—24no—
185Q8—42no—
186Q8—4124no—
187Q8—4122no—
188D4—4124no—
189D4—4122no—
190D4—4122no—
191D4—2064no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1031no—
195C2×C4—1034no—
196C2×C4—1031no—
197C2×C4—1031no—
198C2×C4—4124no—
199C2×C4—4124no—
200C2×C4—2062no—
201C2×C4—2062no—
202C2×C4—2062no—
203C2×C4D4×D10311yescharacteristic
204C2×C4D4×D10311yescharacteristic
205C2×C4C23×D10311yescharacteristic
206C8—22no—
207C8—2062no—
208C22—1032no—
209C22—4122no—
210C22—4122no—
211C22—4122no—
212C22—2061no—
213C22—2061no—
214C22C2×D4×D10311yescharacteristic
215C4—42no—
216C4—42no—
217C4—1032no—
218C4—4122no—
219C4—2061no—
220C4—2061no—
221C4#1569304812yes—
222C4#1569305312yes—
223C4#41×D10312yes—
224C2—8242no—
225C2—2062no—
226C2#124×D10311yescharacteristic
227C2C2×#1569304811yescharacteristic
228C2C2×#1569305311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#487×C103C2
socleC22×C103C22×D4
prime radical#20268342C2
hypercenter#487D103
hypocenterC103#3141
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4⋊Q8×D103C2semidirect
3. #20268152C2semidirect
4. #20268141C2semidirect
5. #20268139C2semidirect
6. #20268138C2semidirect
7. #20267791C2semidirect
8. C4×#13110088C2semidirect
9. #487×C103C2semidirect
115. C103#3141semidirect
120. #487D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202683422
C4⋊Q8×D1032
#202681522
#202681412
#202681392
#202681382
#202677912
C4×#131100882
#487×C1032
#3141103